In TS1 (I don't have any other versions) first you want to make sure from the top down view that your ship is facing left.

Select the part you want to use as a turret (it should be a seperate object) and glue it as a child to whatever it's supposed to be attached to. (Usually the main hull.) Glue as Child usually isn't immediatly visible, it's hidden in the popup menu you get when you hold down the mouse button on Glue as Sibling. (Seen at least one post where someone couldn't find Glue as Child.)
Save and convert. I use ModelView32 for editing 'cause you can see your changes. Make sure the turret submodel has an appropriate subsystem entry in it's properties. (examine any turret on a ship for examples) Go to the turrets section and create a turret, asigning both the Associated/Rotational Submodels to the same turret submodel. (This is where multi-part turrets differs.) Assign at least one firing point and a normal. Save that POF into the models folder, copy a turret entry from another ship, (preferably a ship with the same class flags, like "bomber" "capital" etc.) save the modified table and check the ship out in Fred2.
What do do when things don't work out right:
1. If the turret shows up in Fred2 but you can't assign a weapon to it, change the default weapon. (in the turret's table entry) This happens when you try to assign a weapon to a turret that the ship isn't allowed to have.
2. If the turret doesn't show up, recheck your POF and table entries. Make sure they match. Make sure the turret submodel has a subsystem definition in it's properties.
PS Any turret can be set to rotate. Multi-part turrets just rotate in two different directions.
Edit: Clarified the "default weapon"